Is it a bad idea to have a patio door removed and a new one installed in the middle of the winter? Our temperature has been mostly in the below 32F range and it seems like a cold snap is coming our way. If doing the job is ok, what kind of extra care should be taken in consideration? Should we be worried at all about contraction/expansion of materials?

As long as it only takes a couple of hours to replace the actual door , you should be fine. Any finish painting or caulking are the only issues you may have. Try to do those when it is 40 or above. We do it all the time. If you want them too, they can build a small tent around the work area and heat it. We do that all the time too.
The only thing you need to worry about is pipes freezing, and then thawing out when they have cracked.
Good luck.